The Bivariate Mixture Space: A Compact Spectral Representation of Bivariate Signals

The Fourier Transform (FT) is a widely used analysis tool. However, FT alone is not suited for the analysis of bivariate signals, e.g., stereophonic recordings, because it is not sensitive to the relationship between channels. Different works addressing this problem can be found in the literature; the Bivariate Mixture Space (BMS) is introduced here as an alternative representation to the existing techniques. BMS is still based on the FT and can be thought of as an extension of it, such that the relationship between two signals is considered as additional information in the frequency domain. Despite being simpler than other techniques aimed at representing bivariate signals, this representation is shown to have some desirable characteristics that are absent in traditional representations, which lead to novel ways to perform linear and non-linear decomposition, feature extraction, and data visualization. As a demonstrative application, an Independent Component Analysis algorithm is derived from the BMS, which shows promising results with respect to existing implementations in terms of performance and robustness.